Questions on Exponential Growth & Decay

This is part of the Prelim Maths Extension 1 Syllabus from the topic Calculus: Rates of Change. In this post we will explore Exponential growth and decay understanding the equation. Here we will learn to verify (by substitution) that a solution to the differential equation \frac{dN}{dt} = k(N − P), is () = P + Ae^(kt) for an arbitrary constant, and a fixed quantity, and that the solution is N=P in the case when A = 0.

Let’s check out an application of this: